Figure 6. An electrical ladder-filter circuit.

In this circuit, we make a careful choice of generalised coordinates, which allows us to avoid the explicit use of functions of constraint. We can use the established rules to write down the Lagrangian function for the circuit as shown in Equation 30. We apply the rules for the Euler-Lagrange equation to this Lagrangian function to obtain a pair of ordinary differential equations that describe the dynamics of this circuit.